A mechanical analog for the double sine-Gordon equation

doi:10.1016/0167-2789(85)90007-7

Physica D: Nonlinear Phenomena

Volume 17, Issue 2, October 1985, Pages 227-234

https://doi.org/10.1016/0167-2789(85)90007-7 Get rights and content

Abstract

A mechanical analog for the double sine-Gordon equation is proposed and used to analyze solitary solutions for arbitrary parameter values. The extension of this analog to other equations of the multiple sine-Gordon class is also considered.

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Multidimensional solutions of the nonlinear Klein-Gordon equation
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The nonlinear Klein-Gordon equation in higher dimensions can be reduced to either parabolic, hyperbolic or elliptic nonlinear equations in two independent variables. Some special types of solutions of these reduction equations are presented. The solutions of the reduced parabolic equation possesses two arbitrary functions of x + t. The generalized collapsons and a special type of pulse-like solitary wave solutions which possesses finite energy in the (2 + 1)-dimensional case are just special examples of this type of solutions. Some special solutions of the reduced hyperbolic and elliptic equations are the kink-antikink-like, breather-like and kink-wave-like solutions.
Dynamics and kinetics of solitons in the driven damped double Sine-Gordon equation
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Experimental results are reported for a driven, damped pendulum in which steady and / or alteranting torques were applied by means of a modified brushless, slotless linear motor. The pendulum coordinate was measured with an angular resolver which, in combination with an integrated circuit resolver-to-digital converter, produced readings with fourteen-bit precision. Hysteresis and ac induced steps are observed, as expected, in the torque-velocity characteristics for the pendulum. Poincare sections, power spectra and a state diagram confirm the existence of separate regions of periodic and chaotic behaviour. This system is of particular interest because it can also serve as a mechanical analog of a current biased Josephson junction.

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^†: Dipartimento di Fisica Teorica e sue Metodologie per le Scienze Applicate, Università di Salerno, 84100 Salerno, Italy.

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A mechanical analog for the double sine-Gordon equation

Abstract

J. Phys. A

Phys. Rev. B

J. Phys. C

Phys. Rev. B

Physica

Phys. Rev. B

Phys. Rev. B

J. Phys. C